"As a cancer 'thriver' myself, as many people are, I am very aware of the importance of love, support and family during this journey she is about to begin," the singer-actress, 64, tells Entertainment Tonight. "I want to thank everyone in advance for respecting our privacy during this difficult time."
The Grease star was scheduled to appear at the Las Vegas Flamingo Hotel but has postponed her engagement to be with her family in Los Angeles.
Shortly after her own health battle, the singer-actress told PEOPLE that while she weathered a modified radical mastectomy and a simultaneous saline implant with confidence, the prospect of chemotherapy terrified her. "My fear was that I would die," she said.
To cope, she said, she relied on laughter to maintain her balance during the year of chemotherapy at three-week intervals.
"She had a sense of humor even when they were putting the needle in her veins," Rona, now 69, told PEOPLE back then. "I was amazed at the inner strength Livvy had."